Question

A random sample of n = 25 is obtained from a population with
variance ^{2} , and the sample mean is computed to
be = 70. Consider the null hypothesis H0 : =
80 against H1 : < 80 and compute the p-value when
^{2} = 600.

Answer #1

*Given,*

*n = 25*

*X_bar = 70*

^{2}
=600

*Hypothesis :*

*H _{0}:
=80*

*H _{1}:
< 80*

*First calculate test statistic value*

*
=
^{2}
=
600 = 24.49*

*t= (x_bar -
) /(/n)*

*= (70-80)/(24.49/25)*

*t = - 2.042*

*Calculate df*

*Df =n-1 = 25-1 = 24*

*P value for t test statistic with 24 degree of freedom is
0.0262.*

*P value = 0.0262*

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